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In the diagram, the circle will be dilated by a scale factor of 3 about the origin. The points C. A, and B map to C, A and B' after the dilation. What is
the length of C'B'? Use the distance formula
to help you decide: d=√(x2 − ×₁)² + (x − Y₁)
18-
16-
A.
O B.
24 units
14-
21 units
OC.
15 units
O
12-
D.
E.
5 units
45 units
A=(8,15)
10-
C=(8,10)
Ф
6
B=(12, 13)
0
0
2
4
3-
6
8
10
22
12
14
16



Answer :

To find the length of C'B', we can use the distance formula. Let's calculate it step by step.

First, let's find the coordinates of C' and B' after the dilation. Since the circle is dilated by a scale factor of 3 about the origin, we can multiply the x and y coordinates of C and B by 3.

C' = (3 * 8, 3 * 10) = (24, 30)
B' = (3 * 12, 3 * 13) = (36, 39)

Now, let's use the distance formula to find the length of C'B':

d = √((x2 - x1)² + (y2 - y1)²)

d = √((36 - 24)² + (39 - 30)²)
d = √(12² + 9²)
d = √(144 + 81)
d = √225
d = 15 units

Therefore, the length of C'B' is 15 units.

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